Setting
Let denote a random vector (corresponding to the measurements), taken from a parametrized family of probability density functions or probability mass functions, which depends on the unknown deterministic parameter . The parameter space is partitioned into two disjoint sets and . Let denote the hypothesis that, and let denote the hypothesis that . The binary test of hypotheses is performed using a test function .
meaning that is in force if the measurement and that is in force if the measurement . Note that is a disjoint covering of the measurement space.
Read more about this topic: Uniformly Most Powerful Test
Famous quotes containing the word setting:
“Like plowing, housework makes the ground ready for the germination of family life. The kids will not invite a teacher home if beer cans litter the living room. The family isn’t likely to have breakfast together if somebody didn’t remember to buy eggs, milk, or muffins. Housework maintains an orderly setting in which family life can flourish.”
—Letty Cottin Pogrebin (20th century)
“it is finally as though that thing of monstrous interest
were happening in the sky
but the sun is setting and prevents you from seeing it”
—John Ashbery (b. 1927)
“High from the summit of a craggy cliff,
Hung o’er the deep, such as amazing frowns
On utmost Kilda’s shore, whose lonely race
Resign the setting sun to Indian worlds,
The royal eagle draws his vigorous young”
—James Thomson (1700–1748)